Resumo:
This paper addresses the initial training of Mathematics teachers, investigating the contributions and limitations of Problem Solving (PR) or Problematized Mathematics (PM) for the mathematical training of future teachers. This search is carried out in theses and dissertations that develop empirical research on these approaches. The study reflects on the aspects of school and the mathematical training of future teachers, considering the new realities of school education. It works with the hypothesis that PR and PM are paths to a more effective mathematical training, focused on teaching practice. The research, of a bibliographic nature, examines Brazilian theses and dissertations that adopt the PR or PM approach in the initial training of teachers, and is developed in two phases. The first phase consists of a survey of works on the subject, based on titles and abstracts. The second phase involves a meta-synthesis, with the full reading of the texts and the construction of an interpretative synthesis of the data. The BuscAd tool, developed in Microsoft Excel, was used to organize the search and selection of works. The interpretative synthesis was based on three main focuses: (1) To analyze how RP is approached in empirical research focusing on initial teacher training and to understand its contributions and limitations for mathematics training; (2) To analyze how MP is approached in empirical research focusing on initial teacher training and to understand its contributions and limitations for mathematics training; and (3) To understand intersections and distances between RP and MP based on the research analyzed. The results indicate that in MP, many contributions to the mathematics training of teachers are produced, given its problematizing characteristic and the possibility of producing mathematical knowledge that constantly relates the contents of Academic Mathematics to School Mathematics. On the other hand, as limitations for mathematics training, the challenges of methodological conduct in working with the approach stand out. It is worth noting that, as this is a recent proposal, there are still few studies to be analyzed. For RP, the results show contributions to mathematical education through the dynamics of active student participation in the construction of paths in search of a solution to the problem, making it possible to have a greater meaning of mathematical concepts. As limitations,
